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### Re^3: "-e" and "-d" switches

by nobull (Friar)
 on Mar 24, 2005 at 14:54 UTC ( #442057=note: print w/replies, xml ) Need Help??

in reply to Re^2: "-e" and "-d" switches
in thread "-e" and "-d" switches

Manav wrote:

• -d implies -e
• -e does not imply -d

dragonchild reasponded:

Not quite.

Actually in a formal logic sense your (dragonchild's) four statements are equivalent to manav's two. Or indeed the single statement:

• -d implies -e

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Re^4: "-e" and "-d" switches
by dragonchild (Archbishop) on Mar 24, 2005 at 15:01 UTC
Actually in a formal logic sense your (dragonchild's) four statements are equivalent to manav's two. Or indeed the single statement:

You are absolutely and 100% correct. In the language of the Logical Calculus, my four statements are a verbose version of both manav's two statements and your one statement. However, most people, including most programmers, do not know the Logical Calculus. Coupled with the fact that logic expressed within natural language does not conform to the Logical Calculus and you can see why I would feel compelled to clarify manav's statements.

To further clarify, "implies" has both a formal and an informal definition. The formal definition is as you say. The informal definition for implies is much closer to "if and only if" than "if-then", manav's second statement nothwithstanding. Because the converse is implied when using "implies", I felt the need to explicate the four truth-possibilities, so that there would be no misunderstanding.

Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.

Re^4: "-e" and "-d" switches
by RazorbladeBidet (Friar) on Mar 24, 2005 at 15:00 UTC
-d -> -e implies ~-e -> ~-d

Is there a formal logic representation for "does not necessarily imply"?
--------------
"But what of all those sweet words you spoke in private?"
"Oh that's just what we call pillow talk, baby, that's all."
```~( e -> d ).
"It is not the case that e necessarily implies d", would be the formalized English representation of that logical statement. Implication, within the Logical Calculus, is a fact. "does not necessarily imply" means, formally, "does not imply". That's the he problem with translating formal language to natural language and back again.

Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.

Re^4: "-e" and "-d" switches
by manav (Scribe) on Mar 24, 2005 at 14:58 UTC
Yup. But "-d implies -e" does not imply "-e implies -d" or "-e does not imply -d". As dragonchild puts it succintly, it *says nothing* about reverse implications. Hence the two statements are necessary.

Manav

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